In the cake cutting problem, a cake needs to be divided among players with possibly different valuations for different pieces of the cake. We consider a variation where the cake represents chores that need to be allocated. We assume the players to be work-averse, i.e., intending to get as little of the cake as possible. We further assume that the chores are indivisible and that they are ordered along a line. We seek a fair allocation of the chores.

We study the loss in social welfare due to fairness using the price of fairness concept. Previous work has considered fair division of cakes and chores with non-connected and connected pieces as well as fair division of indivisible contiguous blocks of indivisible items (with positive utility) on a line. We complete the picture by providing price of fairness results for the allocation of contiguous blocks of indivisible chores.

在切蛋糕问题中，一块蛋糕需要在不同的蛋糕块可能具有不同估值的玩家之间进行分配。我们考虑一种变体，其中蛋糕代表需要分配的家务。我们假设玩家厌恶工作，即打算获得尽可能少的蛋糕。我们进一步假设家务是不可分割的，并且它们是沿着一条线排序的。我们寻求公平分配家务。

我们使用公平的价格概念来研究由于公平导致的社会福利损失。以前的工作已经考虑了对蛋糕和家务与非连接件和连接件的公平划分，以及对一条线上不可分割的连续项目（具有正效用）的不可分割的连续块的公平划分。我们通过为分配连续的不可分割的杂务块提供公平结果的价格来完成图片。